FA-87251 / Physics integrator stability / Open access

Sleep timer keeps accumulating across moving frames · case 01

Bodies that move briefly fall asleep mid-motion.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The timer is not reset when the body exceeds the thresholds.

VERIFIED REPAIR

Reset the timer whenever either speed exceeds its threshold.

Unsuccessful approach: Resetting only on linear motion lets a spinning body keep its accumulated sleep time.

Case contract

solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks): per frame, a sleeping body wakes (timer reset) only when that frame's kick is nonzero, else it is skipped. Add the kick [dvx,dvy,domega], damp with 1/(1+dt*c) (linear and angular coefficients), clamp speed magnitude, then accumulate sleep time while |v|<sleep_lin and |omega|<sleep_ang (else reset). When timer>=sleep_time the body sleeps and velocities are zeroed. Return [vx, vy, omega, timer, asleep, frame index slept or -1].

Why this case matters

Game and robotics physics loops depend on integrator update order, step control and stabilization terms; a wrong decision point turns a stable simulation into drifting or exploding motion.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        if timer >= sleep_time:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.06, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.057263, 0.066807, -0.023162, 0.015625, False, -1]], [[[0.07, -0.02], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.058199, -0.016628, 0.773423, 0.0, False, -1]], [[[0.04, -0.03], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0]]], [0.036447, -0.027335, -4.186696, 0.0, False, -1]], [[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.02, 0.01], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[0.0, -0.04], 1.5, 20.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 8, 2], [0, 0, 0], [5, -3, 2]]], [2.222222, -0.631695, 2.793498, 0.0, False, -1]], [[[-0.0, 0.0], 0.99, 2.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0]]], [-1.823636, 7.294543, 0.0, 0.0, False, 1]]], [[[[-0.02, 0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0]]], [-0.018223, 0.091117, 1.454874, 0.0, False, -1]], [[[0.02, 0.03], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.016124, 0.024187, -0.044555, 0.015625, False, -1]], [[[-0.0, -0.03], -0.23, 0.5, 40.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, -1], [0, 0, 0]]], [-1.969112, 0.0, -0.378698, 0.0, False, 6]], [[[0.01, 0.01], 1.94, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, -1]]], [0.0, 0.0, 0.0, 0.015625, True, 8]], [[[1.56, 0.08], 1.64, 80.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[1, 1, 0], [0, 0, -1], [-2, 1, 2], [0, 0, 0], [5, -3, 0.5], [0, 8, 0.5], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.03453, 0.111847, 5.360948, 0.0, False, -1]], [[[0.09, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.068229, -0.053067, -4.27269, 0.0, False, -1]], [[[3.71, -5.39], 0.21, 0.5, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 1, 0], [1, 1, 2]]], [2.924827, 0.667375, 1.580911, 0.0, False, -1]], [[[0.02, -0.02], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, -0.5]]], [0.0, 0.0, -0.380952, 0.0, False, 4]]], [[[[-0.1, -0.05], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [-0.088419, -0.044209, 2.393944, 0.0, False, -1]], [[[-0.02, 0.03], -0.9, 20.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.000347, 0.00052, 0.044934, 0.125, False, -1]], [[[0.01, -0.05], 0.44, 2.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [1, 1, 0.5], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0]]], [-1.386571, 6.97462, 0.222292, 0.0, False, -1]], [[[0.1, 0.08], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.049327, 0.039462, 5.35548, 0.0, False, -1]], [[[-2.45, 1.2], -1.73, 2.0, 40.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 1, 2], [0, 0, 0], [0, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1]]], [-3.52016, -0.911434, -0.528661, 0.0, False, -1]], [[[-1.31, 0.47], 0.1, 80.0, 5.0, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [-2, 8, -1], [0, 0, 0], [0, 0, 0], [1, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[-3.67, -0.63], 0.95, 2.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [-2, 1, 2], [1, -3, 0.5], [-2, -3, 0], [1, 0, 0]]], [-0.643728, -2.182246, 3.014124, 0.0, False, -1]], [[[0.02, -0.01], 1.22, 2.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [1, 8, 0], [0, 0, 0], [0, 0, 0]]], [0.298872, 2.351453, 1.04602, 0.0, False, -1]]], [[[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[1.88, -5.23], -1.53, 0.5, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.793373, -2.207096, -1.9e-05, 0.0, False, -1]], [[[-0.0, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.065775, -5.817074, 0.0, False, -1]], [[[0.03, 0.05], -1.64, 0.5, 40.0, 0.015625, 3.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 3]], [[[2.33, 1.46], 0.09, 80.0, 0.5, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.00023, 5e-06, 1.843775, 0.0, False, -1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[0.06, 0.04], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 6]], [[[-0.02, -0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.019387, -0.096935, 1.465386, 0.0, False, -1]]], [[[[-0.04, 0.1], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0]]], [-0.024972, 0.06243, -2.820937, 0.0, False, -1]], [[[-5.17, -2.18], 1.53, 0.5, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [1, 8, 2], [1, 8, 2], [5, -3, -1], [0, 0, 0], [0, -3, -1]]], [3.17179, 1.717873, -0.302003, 0.0, False, -1]], [[[0.04, 0.05], 1.39, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [1, -3, -1], [5, 1, -1], [-2, 1, 2], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 5]], [[[0.01, -2.66], -0.32, 20.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.167876, -0.023122, 0.992224, 0.0, False, 3]], [[[0.05, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 3.0], [0, 0, -3.0]]], [0.046993, 0.065791, -0.612882, 0.03125, False, -1]], [[[0.01, -0.03], 0.28, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [-1.908081, 7.641838, 0.606234, 0.0, False, -1]], [[[0.05, 0.08], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0]]], [0.031215, 0.049944, 3.612569, 0.0, False, -1]], [[[0.07, -0.09], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, 0]]], [0.064779, -0.083287, 2.951781, 0.0, False, -1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %d" % i, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.057263, 0.066807, -0.023162, 0.03125, False, -1]`	`[0.057263, 0.066807, -0.023162, 0.015625, False, -1]`	Failed
case 1	`[0.058199, -0.016628, 0.773423, 0.015625, False, -1]`	`[0.058199, -0.016628, 0.773423, 0.0, False, -1]`	Failed
case 2	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	Passed
case 3	`[0.013154, 0.026308, -0.658704, 0.0625, False, -1]`	`[0.013154, 0.026308, -0.658704, 0.0, False, -1]`	Failed
case 4	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	Passed
case 5	`[0.285714, -0.244898, 0.0, 0.0625, False, 3]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Failed
case 6	`[2.222222, -0.631695, 2.793498, 0.0625, False, -1]`	`[2.222222, -0.631695, 2.793498, 0.0, False, -1]`	Failed
case 7	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	Passed

SHA-256 / a8ef9918230e5db404a9df13bc1307774fc087bb377cc068f40cd69b027e7eac

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        elif math.hypot(vx, vy) >= sleep_lin:
            timer = 0.0
        if timer >= sleep_time:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.06, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.057263, 0.066807, -0.023162, 0.015625, False, -1]], [[[0.07, -0.02], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.058199, -0.016628, 0.773423, 0.0, False, -1]], [[[0.04, -0.03], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0]]], [0.036447, -0.027335, -4.186696, 0.0, False, -1]], [[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.02, 0.01], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[0.0, -0.04], 1.5, 20.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 8, 2], [0, 0, 0], [5, -3, 2]]], [2.222222, -0.631695, 2.793498, 0.0, False, -1]], [[[-0.0, 0.0], 0.99, 2.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0]]], [-1.823636, 7.294543, 0.0, 0.0, False, 1]]], [[[[-0.02, 0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0]]], [-0.018223, 0.091117, 1.454874, 0.0, False, -1]], [[[0.02, 0.03], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.016124, 0.024187, -0.044555, 0.015625, False, -1]], [[[-0.0, -0.03], -0.23, 0.5, 40.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, -1], [0, 0, 0]]], [-1.969112, 0.0, -0.378698, 0.0, False, 6]], [[[0.01, 0.01], 1.94, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, -1]]], [0.0, 0.0, 0.0, 0.015625, True, 8]], [[[1.56, 0.08], 1.64, 80.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[1, 1, 0], [0, 0, -1], [-2, 1, 2], [0, 0, 0], [5, -3, 0.5], [0, 8, 0.5], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.03453, 0.111847, 5.360948, 0.0, False, -1]], [[[0.09, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.068229, -0.053067, -4.27269, 0.0, False, -1]], [[[3.71, -5.39], 0.21, 0.5, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 1, 0], [1, 1, 2]]], [2.924827, 0.667375, 1.580911, 0.0, False, -1]], [[[0.02, -0.02], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, -0.5]]], [0.0, 0.0, -0.380952, 0.0, False, 4]]], [[[[-0.1, -0.05], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [-0.088419, -0.044209, 2.393944, 0.0, False, -1]], [[[-0.02, 0.03], -0.9, 20.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.000347, 0.00052, 0.044934, 0.125, False, -1]], [[[0.01, -0.05], 0.44, 2.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [1, 1, 0.5], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0]]], [-1.386571, 6.97462, 0.222292, 0.0, False, -1]], [[[0.1, 0.08], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.049327, 0.039462, 5.35548, 0.0, False, -1]], [[[-2.45, 1.2], -1.73, 2.0, 40.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 1, 2], [0, 0, 0], [0, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1]]], [-3.52016, -0.911434, -0.528661, 0.0, False, -1]], [[[-1.31, 0.47], 0.1, 80.0, 5.0, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [-2, 8, -1], [0, 0, 0], [0, 0, 0], [1, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[-3.67, -0.63], 0.95, 2.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [-2, 1, 2], [1, -3, 0.5], [-2, -3, 0], [1, 0, 0]]], [-0.643728, -2.182246, 3.014124, 0.0, False, -1]], [[[0.02, -0.01], 1.22, 2.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [1, 8, 0], [0, 0, 0], [0, 0, 0]]], [0.298872, 2.351453, 1.04602, 0.0, False, -1]]], [[[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[1.88, -5.23], -1.53, 0.5, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.793373, -2.207096, -1.9e-05, 0.0, False, -1]], [[[-0.0, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.065775, -5.817074, 0.0, False, -1]], [[[0.03, 0.05], -1.64, 0.5, 40.0, 0.015625, 3.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 3]], [[[2.33, 1.46], 0.09, 80.0, 0.5, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.00023, 5e-06, 1.843775, 0.0, False, -1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[0.06, 0.04], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 6]], [[[-0.02, -0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.019387, -0.096935, 1.465386, 0.0, False, -1]]], [[[[-0.04, 0.1], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0]]], [-0.024972, 0.06243, -2.820937, 0.0, False, -1]], [[[-5.17, -2.18], 1.53, 0.5, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [1, 8, 2], [1, 8, 2], [5, -3, -1], [0, 0, 0], [0, -3, -1]]], [3.17179, 1.717873, -0.302003, 0.0, False, -1]], [[[0.04, 0.05], 1.39, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [1, -3, -1], [5, 1, -1], [-2, 1, 2], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 5]], [[[0.01, -2.66], -0.32, 20.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.167876, -0.023122, 0.992224, 0.0, False, 3]], [[[0.05, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 3.0], [0, 0, -3.0]]], [0.046993, 0.065791, -0.612882, 0.03125, False, -1]], [[[0.01, -0.03], 0.28, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [-1.908081, 7.641838, 0.606234, 0.0, False, -1]], [[[0.05, 0.08], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0]]], [0.031215, 0.049944, 3.612569, 0.0, False, -1]], [[[0.07, -0.09], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, 0]]], [0.064779, -0.083287, 2.951781, 0.0, False, -1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %d" % i, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.057263, 0.066807, -0.023162, 0.03125, False, -1]`	`[0.057263, 0.066807, -0.023162, 0.015625, False, -1]`	Failed
case 1	`[0.058199, -0.016628, 0.773423, 0.015625, False, -1]`	`[0.058199, -0.016628, 0.773423, 0.0, False, -1]`	Failed
case 2	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	Passed
case 3	`[0.013154, 0.026308, -0.658704, 0.0625, False, -1]`	`[0.013154, 0.026308, -0.658704, 0.0, False, -1]`	Failed
case 4	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	Passed
case 5	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Passed
case 6	`[2.222222, -0.631695, 2.793498, 0.0, False, -1]`	`[2.222222, -0.631695, 2.793498, 0.0, False, -1]`	Passed
case 7	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	Passed

SHA-256 / 551826f6c5742c54fc700ef1f7ab9666d52d7de170c3eadfb13dc36aa179365b

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(v, omega, lin_damp, ang_damp, dt, max_speed, sleep_lin, sleep_ang, sleep_time, kicks):
    vx, vy = v
    w = omega
    timer = 0.0
    asleep = False
    slept_at = -1
    for f, (ax, ay, aw) in enumerate(kicks):
        if asleep:
            if ax or ay or aw:
                asleep = False
                timer = 0.0
            else:
                continue
        vx += ax
        vy += ay
        w += aw
        dl = 1.0 / (1.0 + dt * lin_damp)
        vx *= dl
        vy *= dl
        w *= 1.0 / (1.0 + dt * ang_damp)
        sp = math.hypot(vx, vy)
        if sp > max_speed:
            s = max_speed / sp
            vx *= s
            vy *= s
        if math.hypot(vx, vy) < sleep_lin and abs(w) < sleep_ang:
            timer += dt
        else:
            timer = 0.0
        if timer >= sleep_time:
            asleep = True
            slept_at = f
            vx = vy = w = 0.0
    return [round(vx, 6), round(vy, 6), round(w, 6), round(timer, 6), asleep, slept_at]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[[[[0.06, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5]]], [0.057263, 0.066807, -0.023162, 0.015625, False, -1]], [[[0.07, -0.02], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0.5], [0, 0, 0]]], [0.058199, -0.016628, 0.773423, 0.0, False, -1]], [[[0.04, -0.03], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0]]], [0.036447, -0.027335, -4.186696, 0.0, False, -1]], [[[0.03, 0.06], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0]]], [0.013154, 0.026308, -0.658704, 0.0, False, -1]], [[[0.02, 0.01], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, -0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 3]], [[[-0.42, 3.07], 0.58, 80.0, 40.0, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0], [0, -3, 0], [1, 0, 0]]], [0.285714, 0.0, 0.0, 0.03125, False, 5]], [[[0.0, -0.04], 1.5, 20.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [0, 8, 2], [0, 0, 0], [5, -3, 2]]], [2.222222, -0.631695, 2.793498, 0.0, False, -1]], [[[-0.0, 0.0], 0.99, 2.0, 0.5, 0.015625, 8.0, 2.0, 1.0, 0.03125, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0], [0, 0, 0]]], [-1.823636, 7.294543, 0.0, 0.0, False, 1]]], [[[[-0.02, 0.1], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0]]], [-0.018223, 0.091117, 1.454874, 0.0, False, -1]], [[[0.02, 0.03], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, -3.0], [0, 0, 3.0]]], [0.016124, 0.024187, -0.044555, 0.015625, False, -1]], [[[-0.0, -0.03], -0.23, 0.5, 40.0, 0.015625, 8.0, 0.5, 0.3, 0.03125, [[0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1], [0, 0, 0], [0, 0, 0], [-2, 0, -1], [0, 0, 0]]], [-1.969112, 0.0, -0.378698, 0.0, False, 6]], [[[0.01, 0.01], 1.94, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, 0, -1]]], [0.0, 0.0, 0.0, 0.015625, True, 8]], [[[1.56, 0.08], 1.64, 80.0, 0.5, 0.015625, 3.0, 2.0, 1.0, 0.03125, [[1, 1, 0], [0, 0, -1], [-2, 1, 2], [0, 0, 0], [5, -3, 0.5], [0, 8, 0.5], [0, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.03453, 0.111847, 5.360948, 0.0, False, -1]], [[[0.09, -0.07], 0.0, 2.0, 0.5, 0.015625, 8.0, 0.5, 0.3, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.068229, -0.053067, -4.27269, 0.0, False, -1]], [[[3.71, -5.39], 0.21, 0.5, 5.0, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 1, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 1, 0], [1, 1, 2]]], [2.924827, 0.667375, 1.580911, 0.0, False, -1]], [[[0.02, -0.02], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [0, 0, -0.5], [0, 0, 0], [0, 0, 0.5], [0, 0, 0], [0, 0, -0.5]]], [0.0, 0.0, -0.380952, 0.0, False, 4]]], [[[[-0.1, -0.05], 0.0, 2.0, 5.0, 0.015625, 8.0, 0.5, 1.0, 0.03125, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 0]]], [-0.088419, -0.044209, 2.393944, 0.0, False, -1]], [[[-0.02, 0.03], -0.9, 20.0, 40.0, 0.0625, 8.0, 2.0, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.000347, 0.00052, 0.044934, 0.125, False, -1]], [[[0.01, -0.05], 0.44, 2.0, 5.0, 0.0625, 8.0, 2.0, 1.0, 0.1875, [[0, 0, 0], [1, 1, 0.5], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 8, 0], [0, 0, 0]]], [-1.386571, 6.97462, 0.222292, 0.0, False, -1]], [[[0.1, 0.08], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 1.0, 0.125, [[0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 1.5]]], [0.049327, 0.039462, 5.35548, 0.0, False, -1]], [[[-2.45, 1.2], -1.73, 2.0, 40.0, 0.015625, 8.0, 0.5, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [-2, 1, 2], [0, 0, 0], [0, -3, 0], [0, 0, 0], [0, 0, 0], [0, 0, -1]]], [-3.52016, -0.911434, -0.528661, 0.0, False, -1]], [[[-1.31, 0.47], 0.1, 80.0, 5.0, 0.0625, 8.0, 2.0, 0.3, 0.125, [[0, 0, 0], [-2, 8, -1], [0, 0, 0], [0, 0, 0], [1, 0, 0.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.125, True, 5]], [[[-3.67, -0.63], 0.95, 2.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0], [0, 0, 0], [-2, 1, 2], [1, -3, 0.5], [-2, -3, 0], [1, 0, 0]]], [-0.643728, -2.182246, 3.014124, 0.0, False, -1]], [[[0.02, -0.01], 1.22, 2.0, 0.5, 0.0625, 3.0, 2.0, 1.0, 0.125, [[0, 0, 0], [0, 0, 0], [1, 8, 0], [0, 0, 0], [0, 0, 0]]], [0.298872, 2.351453, 1.04602, 0.0, False, -1]]], [[[[-0.0, 0.01], -1.88, 2.0, 40.0, 0.015625, 8.0, 2.0, 1.0, 0.015625, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [5, 8, 0]]], [4.239992, 6.783986, 0.0, 0.0, False, 1]], [[[1.88, -5.23], -1.53, 0.5, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.793373, -2.207096, -1.9e-05, 0.0, False, -1]], [[[-0.0, 0.07], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 1.5], [0, 0, -1.5], [0, 0, -1.5], [0, 0, 0], [0, 0, -1.5]]], [0.0, 0.065775, -5.817074, 0.0, False, -1]], [[[0.03, 0.05], -1.64, 0.5, 40.0, 0.015625, 3.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.046875, True, 3]], [[[2.33, 1.46], 0.09, 80.0, 0.5, 0.03125, 3.0, 2.0, 1.0, 0.09375, [[0, 0, 0], [0, 0, 0], [5, 0, 2], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0], [0, 0, 0]]], [0.00023, 5e-06, 1.843775, 0.0, False, -1]], [[[-0.04, -0.04], 0.45, 20.0, 40.0, 0.0625, 3.0, 0.5, 0.3, 0.0625, [[0, 1, -1], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.0625, True, 0]], [[[0.06, 0.04], 0.0, 0.5, 5.0, 0.0625, 8.0, 0.5, 1.0, 0.1875, [[0, 0, -1.5], [0, 0, 1.5], [0, 0, 1.5], [0, 0, 0], [0, 0, 0], [0, 0, -1.5], [0, 0, 1.5], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.1875, True, 6]], [[[-0.02, -0.1], 0.0, 0.5, 0.5, 0.015625, 8.0, 0.5, 1.0, 0.046875, [[0, 0, 0], [0, 0, 1.5], [0, 0, 0], [0, 0, 0]]], [-0.019387, -0.096935, 1.465386, 0.0, False, -1]]], [[[[-0.04, 0.1], 0.0, 2.0, 0.5, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 0], [0, 0, -3.0], [0, 0, 0]]], [-0.024972, 0.06243, -2.820937, 0.0, False, -1]], [[[-5.17, -2.18], 1.53, 0.5, 40.0, 0.015625, 8.0, 2.0, 0.3, 0.015625, [[0, 0, 0], [1, 8, 2], [1, 8, 2], [5, -3, -1], [0, 0, 0], [0, -3, -1]]], [3.17179, 1.717873, -0.302003, 0.0, False, -1]], [[[0.04, 0.05], 1.39, 20.0, 40.0, 0.03125, 8.0, 2.0, 0.3, 0.03125, [[0, 0, 0], [1, -3, -1], [5, 1, -1], [-2, 1, 2], [0, 0, 0], [0, 0, 0]]], [0.0, 0.0, 0.0, 0.03125, True, 5]], [[[0.01, -2.66], -0.32, 20.0, 0.5, 0.0625, 3.0, 0.5, 0.3, 0.125, [[0, 0, 0.5], [0, 0, 0], [0, 0, 0], [0, 0, 0], [1, -3, -1], [0, 0, 0], [0, 0, 0], [-2, 0, 2], [0, 0, 0], [0, 0, 0]]], [-0.167876, -0.023122, 0.992224, 0.0, False, 3]], [[[0.05, 0.07], 0.0, 0.5, 5.0, 0.03125, 8.0, 0.5, 1.0, 0.0625, [[0, 0, 3.0], [0, 0, -3.0], [0, 0, 3.0], [0, 0, -3.0]]], [0.046993, 0.065791, -0.612882, 0.03125, False, -1]], [[[0.01, -0.03], 0.28, 0.5, 5.0, 0.015625, 8.0, 2.0, 1.0, 0.046875, [[0, 0, 0], [-2, 8, 0.5], [0, 0, 0], [0, 0, 0]]], [-1.908081, 7.641838, 0.606234, 0.0, False, -1]], [[[0.05, 0.08], 0.0, 2.0, 5.0, 0.0625, 8.0, 0.5, 0.3, 0.1875, [[0, 0, 0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0]]], [0.031215, 0.049944, 3.612569, 0.0, False, -1]], [[[0.07, -0.09], 0.0, 0.5, 0.5, 0.03125, 8.0, 0.5, 1.0, 0.09375, [[0, 0, -3.0], [0, 0, 3.0], [0, 0, 0], [0, 0, 3.0], [0, 0, 0]]], [0.064779, -0.083287, 2.951781, 0.0, False, -1]]]]
for i, (args, expected) in enumerate(fixtures[N-1]):
    check("case %d" % i, solve(*args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
case 0	`[0.057263, 0.066807, -0.023162, 0.015625, False, -1]`	`[0.057263, 0.066807, -0.023162, 0.015625, False, -1]`	Passed
case 1	`[0.058199, -0.016628, 0.773423, 0.0, False, -1]`	`[0.058199, -0.016628, 0.773423, 0.0, False, -1]`	Passed
case 2	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	`[0.036447, -0.027335, -4.186696, 0.0, False, -1]`	Passed
case 3	`[0.013154, 0.026308, -0.658704, 0.0, False, -1]`	`[0.013154, 0.026308, -0.658704, 0.0, False, -1]`	Passed
case 4	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	`[0.0, 0.0, 0.0, 0.03125, True, 3]`	Passed
case 5	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	`[0.285714, 0.0, 0.0, 0.03125, False, 5]`	Passed
case 6	`[2.222222, -0.631695, 2.793498, 0.0, False, -1]`	`[2.222222, -0.631695, 2.793498, 0.0, False, -1]`	Passed
case 7	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	`[-1.823636, 7.294543, 0.0, 0.0, False, 1]`	Passed

SHA-256 / 0b7f2a07880f3e7af60efea4e908a4a42d66317ace977635dd099301dae3d4aa

Verification & scope

A deterministic bounded teaching model with stipulated toy conventions and rounded float output; not a production physics engine or a proof of numerical stability. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:50:57.039638+00:00.

Case digest / 5a240cbb1ab1fcaca42133bf93e1b9d7b4cecf26766217dd803946ebae64a20f